Annotation of OpenXM_contrib/PHC/Ada/Root_Counts/Dynlift/cayley_trick.ads, Revision 1.1
1.1 ! maekawa 1: with Standard_Integer_Vectors; use Standard_Integer_Vectors;
! 2: with Arrays_of_Integer_Vector_Lists; use Arrays_of_Integer_Vector_Lists;
! 3: with Triangulations; use Triangulations;
! 4: with Integer_Mixed_Subdivisions; use Integer_Mixed_Subdivisions;
! 5:
! 6: package Cayley_Trick is
! 7:
! 8: -- DESCRIPTION :
! 9: -- This procedure provides some routines for constructing a mixed
! 10: -- subdivision by applicaton of the dynamic lifting algorithm to
! 11: -- the Cayley trick.
! 12:
! 13: -- OPTIONS :
! 14: -- 1. choice of the order of the points
! 15: -- 2. for vertices or not: allows to add interior points
! 16: -- 3. with maximum value on the lifting function or not
! 17:
! 18: -- VERSIONS :
! 19: -- 1. with or without output generics, before flattening or after new cell
! 20: -- 2. with as result only the mixed subdivision or the whole triangulation
! 21:
! 22: -- BASIC VERSION : WITHOUT OUTPUT GENERICS :
! 23:
! 24: procedure Dynamic_Cayley
! 25: ( n : in natural; mix : in Vector;
! 26: supports : in Array_of_Lists; order,inter : in boolean;
! 27: maxli : in natural; lifted : out Array_of_Lists;
! 28: mixsub : out Mixed_Subdivision; numtri : out natural );
! 29:
! 30: procedure Dynamic_Cayley
! 31: ( n : in natural; mix : in Vector;
! 32: supports : in Array_of_Lists; order,inter : in boolean;
! 33: maxli : in natural; lifted : out Array_of_Lists;
! 34: t : in out Triangulation );
! 35:
! 36: -- DESCRIPTION :
! 37: -- Application of the dynamic lifting algorithm to the Cayley trick.
! 38:
! 39: -- ON ENTRY :
! 40: -- n length of the vectors in the supports;
! 41: -- mix type of mixture;
! 42: -- supports lists of integer vector of length n;
! 43: -- order if true, then the points are already ordered and will
! 44: -- be processed like they occur in the list,
! 45: -- if false, then a random order will be chosen;
! 46: -- inter if true, then the list may contain interior points,
! 47: -- i.e. points x in conv(l\{x}),
! 48: -- if false, no interior points occur in the list;
! 49: -- maxli maximum value of the lifting function,
! 50: -- if = 0, then no flattening will be applied,
! 51: -- i.e. there is no maximum lifting value,
! 52: -- if > 0, then no points will be given a lifting value
! 53: -- greater than maxli.
! 54:
! 55: -- ON RETURN :
! 56: -- lifted the lifted supports;
! 57: -- mixsub the mixed subdivision;
! 58: -- numtri number of simplices in the triangulation of the
! 59: -- auxiliary polytope;
! 60: -- t triangulation of the auxiliary polytope.
! 61:
! 62: -- EXTENDED VERSIONS : WITH OUTPUT GENERICS
! 63:
! 64: generic
! 65: with procedure Before_Flattening
! 66: ( mixsub : in out Mixed_Subdivision;
! 67: lifted : in Array_of_Lists );
! 68:
! 69: -- DESCRIPTION :
! 70: -- Before flattening, the current mixed subdivision with
! 71: -- the current lists of lifted points are given.
! 72:
! 73: procedure Dynamic_Cayley_with_Flat
! 74: ( n : in natural; mix : in Vector;
! 75: supports : in Array_of_Lists; order,inter : in boolean;
! 76: maxli : in natural; lifted : out Array_of_Lists;
! 77: mixsub : out Mixed_Subdivision; numtri : out natural );
! 78:
! 79: generic
! 80: with procedure Before_Flattening
! 81: ( mixsub : in out Mixed_Subdivision;
! 82: lifted : in Array_of_Lists );
! 83: procedure Dynamic_Cayley_with_Flatt
! 84: ( n : in natural; mix : in Vector;
! 85: supports : in Array_of_Lists; order,inter : in boolean;
! 86: maxli : in natural; lifted : out Array_of_Lists;
! 87: t : in out Triangulation );
! 88:
! 89: -- DESCRIPTION :
! 90: -- Application of the dynamic lifting algorithm to the Cayley trick.
! 91: -- Before flattening, the generic procedure will be invoked.
! 92: -- The parameters have the same meaning as in the basic version.
! 93:
! 94: generic
! 95: with procedure Process_New_Cells
! 96: ( mixsub : in out Mixed_Subdivision;
! 97: i : in natural; point : in vector );
! 98:
! 99: -- DESCRIPTION :
! 100: -- After the addition of a new point to the ith component,
! 101: -- this point together with the new mixed cells are returned.
! 102: -- For the initial cell, i=0.
! 103:
! 104: procedure Dynamic_Cayley_with_New
! 105: ( n : in natural; mix : in Vector;
! 106: supports : in Array_of_Lists; order,inter : in boolean;
! 107: maxli : in natural; lifted : out Array_of_Lists;
! 108: mixsub : out Mixed_Subdivision; numtri : out natural );
! 109:
! 110: generic
! 111: with procedure Process_New_Cells
! 112: ( mixsub : in out Mixed_Subdivision;
! 113: i : in natural; point : in vector );
! 114: procedure Dynamic_Cayley_with_Newt
! 115: ( n : in natural; mix : in Vector;
! 116: supports : in Array_of_Lists; order,inter : in boolean;
! 117: maxli : in natural; lifted : out Array_of_Lists;
! 118: t : in out Triangulation );
! 119:
! 120: -- DESCRIPTION :
! 121: -- Application of the dynamic lifting algorithm to the Cayley trick.
! 122: -- After each addition of a point, the generic procedure will
! 123: -- be invoked.
! 124: -- The parameters have the same meaning as in the basic version.
! 125:
! 126: generic
! 127: with procedure Before_Flattening
! 128: ( mixsub : in out Mixed_Subdivision;
! 129: lifted : in Array_of_Lists );
! 130:
! 131: -- DESCRIPTION :
! 132: -- Before flattening, the current mixed subdivision with
! 133: -- the current lists of lifted points are given.
! 134:
! 135: with procedure Process_New_Cells
! 136: ( mixsub : in out Mixed_Subdivision;
! 137: i : in natural; point : in vector );
! 138:
! 139: -- DESCRIPTION :
! 140: -- After the addition of a new point to the ith component,
! 141: -- this point together with the new simplices are returned.
! 142: -- For the initial cell, i=0.
! 143:
! 144: procedure Dynamic_Cayley_with_Flat_and_New
! 145: ( n : in natural; mix : in Vector;
! 146: supports : in Array_of_Lists; order,inter : in boolean;
! 147: maxli : in natural; lifted : out Array_of_Lists;
! 148: mixsub : out Mixed_Subdivision; numtri : out natural );
! 149:
! 150: generic
! 151: with procedure Before_Flattening
! 152: ( mixsub : in out Mixed_Subdivision;
! 153: lifted : in Array_of_Lists );
! 154: with procedure Process_New_Cells
! 155: ( mixsub : in out Mixed_Subdivision;
! 156: i : in natural; point : in vector );
! 157: procedure Dynamic_Cayley_with_Flat_and_Newt
! 158: ( n : in natural; mix : in Vector;
! 159: supports : in Array_of_Lists; order,inter : in boolean;
! 160: maxli : in natural; lifted : out Array_of_Lists;
! 161: t : in out Triangulation );
! 162:
! 163:
! 164: -- DESCRIPTION :
! 165: -- Application of the dynamic lifting algorithm to the list l.
! 166: -- Before flattening, the first generic procedure will be invoked.
! 167: -- After each addition of a point, the second generic procedure
! 168: -- will be invoked.
! 169: -- The parameters have the same meaning as in the basic version.
! 170:
! 171: end Cayley_Trick;
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